Question

Suppose x has a distribution with μ = 23 and σ = 15.

(a) If a random sample of size n = 32 is drawn, find μx, σ x and P(23 ≤ x ≤ 25). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(23 ≤ x ≤ 25) =

(b) If a random sample of size n = 73 is drawn, find μx, σ x and P(23 ≤ x ≤ 25). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(23 ≤ x ≤ 25) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)

The standard deviation of part (b) (is smaller than, larger than or same as) is part (a) because of the (smaller, larger or same) sample size. Therefore, the distribution about μx is (wider, narrower or same) .

Answer 1